Incorporating potential catastrophic consequences into integrated assessment models of climate change has been a top priority of policymakers and modelers alike. We review the current state of scientific understanding regarding three frequently mentioned geophysical catastrophes, with a view toward their implications for integrated assessment modeling. This review finds inadequacies in widespread model assumptions regarding the nature of catastrophes themselves and climate change impacts more generally. The possibility of greatly postponed consequences from near- and medium-term actions suggests that standard discounting practices are inappropriate for the analysis of climate catastrophe. Careful consideration of paleoclimate and geophysical modeling evidence regarding the possibility of changes in ocean circulation suggests a reframing of the source of climate change damages in economic models, placing changes in climate predictability, rather than gradual changes in mean values, at the focus of economic damage assessments. The implications of decreases in predictability for the modeling of adaptation are further discussed.